 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ib/paper-4/8d/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Gaussian elimination without pivoting gives

A = LU, L = 1212013200120001, U = 100021001330 226 λ - 20 .

Thus

det A = 3 (λ - 20)

and the solution is unique exactly when $λ \neq = 20$ .

For

λ = 20

L y = b

gives

y = (1, 1, 3, μ - 10)^{T}

Ux = y

requires

μ = 10

x = (4 - 8 t, 4 t - 2, 1 - 2 t, t)^{T}, t \in R .

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